
Physics at atomic scales contains many surprises.
According to the quantum theory, light has momentum, just like matter. And matter (such as electrons) can exhibit both wave and particle behavior, just as you learned earlier about light.
In quantum physics, the position and momentum of a particle cannot be known simultaneously to high precision.
Instead, there is an inherent uncertainty in how well we can know position and momentum (or energy and time).
But perhaps the strangest feature of the quantum world is that many of the properties of particles are probabilistic or statistical.
You don’t know where an electron is located; you only have probabilities for its being in various locations.

uncertainty principle, wave function, stimulated emission, laser, spontaneous emission


 
$$\text{\Delta}p\text{\Delta}x\ge \frac{h}{4\pi}$$

 $$\text{\Delta}E\text{\Delta}t\ge \frac{h}{4\pi}$$



Review problems and questions 

 In the electron version of the double slit experiment, electrons are detected on a screen and show an interference pattern. Does each individual electron pass through one or the other slit?

No. Each electron is passing, in part, through both slits and interfering with itself. This is one of those quantum physics paradoxes: Matter behaves like a wave, and the location of matter at any given time is indeterminate (to some level). Since we don’t know the location of the electron when it got to the slits, it had some probability of passing through each slit—so it passed through both!

 Imagine a modification to the electron double slit experiment where you place a detector next to one slit to determine at the location of the slit whether or not each electron passed through that slit. Will the electrons still show an interference pattern on the screen?

No; the electrons will show a reduced interference pattern or none whatsoever! One of the headscratching features of quantum physics is that, once you have localized a particle (such as by determining whether it passes through a narrow slit) you prevent it from showing the wave behavior. This is called the complementarity principle, that an object cannot simultaneously exhibit properties of both a particle and a wave.

 One of the bestknown paradoxes of quantum physics is called “Schrödinger’s cat.” Imagine a black box that contains a cat and a randomized device that, if triggered, kills the cat. If you wait a while, you won’t know whether the device has triggered and killed the cat, or whether the cat is still alive. If you open up the box and look inside, then you can tell whether the cat is alive or dead. But before you open up the box, according to the concepts of quantum physics, is the cat alive or dead?

According to the concepts of quantum physics, the cat is partially alive and partially dead until you look inside the box. The cat has some probability of being alive and some probability of being dead, so it is partially both dead and alive until you open the box.

 Mauro studied quantum physics and has what he thinks is a great idea for a new invention he calls the Earth Tunneler: a tunneling device that will allow him to pass through the solid Earth and show up on the far side. He insists that the concepts of quantum tunneling will allow him to tunnel straight through the Earth. Is his invention a solid idea?

No. Quantum tunneling is a feature of particles at the atomic scale, while Mauro’s invention would work at macroscopic scales. Don’t invest money in his scheme!

 Research the two kinds of laser eye surgery called LASIK and PRK. What wavelengths of lasers are used in them? What is the laser used for?

Both use a pulsing, ultraviolet light laser at around 150 to 190 nm that breaks up tissue on the surface of the eye or cornea.

 If you want to know the position of an electron to within the radius of the atom of around 0.5 angstrom (0.5×10^{−10} m), what is the best precision with which you can know its velocity?

Answer: Δv ≥ 1.2×10^{6} m/s
Start with the Heisenberg uncertainty principle equation and solve for momentum:$$\text{\Delta}p=m\text{\Delta}v\ge \frac{h}{4\pi \Delta x}$$Then use p = mv to solve for velocity:$$\text{\Delta}v\ge \frac{h}{4\pi {m}_{e}\text{\Delta}x}$$Inserting the values gives$$\text{\Delta}v\ge \frac{6.63\times {10}^{34}\text{Js}}{4\pi (9.1\times {10}^{31}\text{kg})(0.5\times {10}^{10}\text{m})}=1.2\times {10}^{6}\text{m/s}$$

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